Proof:
Theorem: The family of CFLs is closed under union, concatenation, iteration.
Closure properties
• Let L1, L2 be two CFLs.
• Then, there exist two CFGs G1, G2 such that
   L(G1) = L1, L(G2) = L2;
• Construct grammars
• Gu such that L(Gu) = L(G1) È L(G2)
• Gc such that L(Gc) = L(G2) . L(G2)
• Gi such that L(Gi)  = L(G1)*
by using the previous three algorithms
• Every CFG denotes CFL, so
• L1 L2,  L1 È  L2,  L1* are CFLs.
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